Abstract: I'll first review the symplectic geometrical part of coadjoint orbits and the connection to symplectic singularities.Then I'll move to the classification of nilpotent orbits and their crepant resolutions given by Springer maps. Different crepant resolutions are connected by stratified Mukai flops. Although we have a clear understanding of the geometry of these flops, the derived equivalence between them is still mysterious.If time permits, I'll also describe a construction of a new family of 4-dimensional isolated symplectic singularities with trivial local fundamental groups, which answers a question of Beauville raised in 2000.